Florida Dept. of EducationBureau of Curriculum & Instruction1 Math Coaches/Contact Meeting December 14, 2012 Course Descriptions/Learning Goals

Florida’s CCSS Implementation Plan Florida Dept. of EducationBureau of Curriculum & Instruction2 Full Implementation Grade K Begin Implementation of Literacy Standards in ALL Content Areas for Grades Begin Implementation of Rich and Complex Text and Informational Text for Grades K-12 Phase 1 ( ) Full Implementation Grades K-1 (BCPS K-2) Full Implementation of Literacy Standards in ALL Content Areas for Grades Continue Implementation of Rich and Complex Text and Informational Text for Grades K-12 Phase 2 ( ) Full Implementation Grades K-2 Implementation of a Blended Curriculum (CCSS and Supplemental NGSSS Aligned to FCAT 2.0 and EOCs) for Grades 3-12 Continue Implementation of Rich and Complex Text and Informational Text for Grades K-12 Phase 3 ( ) Full Implementation Grades K-12 PARCC Assessments Aligned to CCSS Phase 4 ( )

Course Requirements and Standards Curriculum Mapping in Layers “Chunks” or Big Ideas Florida Dept. of EducationBureau of Curriculum & Instruction3 Major Learning Goals Identify major learning goals for a specific course by integrating across content areas and “chunking” the standards into a few big ideas Develop a projected timeline for instruction by mapping the major learning goals across the semester or year as appropriate for the course Progression Scales for Major Learning Goals Describe the learning progressions and develop a scale or rubric for at least one of the major learning goals for the course (Day 2) Progress Monitoring Assessments Describe at least one assessment item that is appropriate for each of the levels beginning with Level 2 on the learning progression scale Draft a blueprint for future progress monitoring assessments based upon the curriculum map (or pacing guide) and anticipated learning progressions (Day 2)

Current Way of Work Given the full implementation of Florida’s NGSSS what three words might we use to describe instruction in Florida? – Standards-Based Instruction What often guides the development of our curriculum maps or pacing guides? – Test Item Specifications What tools might we use to monitor the progress of our students? – Focus Mini-Assessments (Benchmark Assessments) Florida Dept. of EducationBureau of Curriculum & Instruction4

Florida Transitions to Common Core State Standards Next Generation Standards Standards-based instruction Test item specifications guide development of curriculum maps Focus mini-assessments aligned to individual benchmarks and used to monitor student progress Teaching benchmarks in isolation results in long lists of tasks to master Common Core Standards Standards-based instruction facilitated by learning goals Big ideas and learning goals guide the development of curriculum maps Learning progressions or scales describe expectations for student progress in attaining the learning goals Assessments used to monitor student progress are aligned directly to the learning progressions or scales Teaching big ideas narrows the focus and allows students to delve deeper for a greater depth of understanding Florida Dept. of EducationBureau of Curriculum & Instruction5

Common Core State Standards for Mathematics Domains are larger groups of related standards. Standards from different domains may sometimes be closely related Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. Standards define what students should understand and be able to do.

Domains for K-12 K HS Counting and Cardinality (CC) Number and Quantity Number and Operations in Base Ten (NBT)The Number System Number and Operations-Fractions (NF) Ratios and Proportional Relationships (RP) Operations and Algebraic Thinking (OA) Functions (F) Expressions and Equations (EE) Algebra (A) Geometry (G) Measurement and Data (MD) Statistics and Probability (SP)

High School Conceptual Categories Number and Quantity (N) Algebra (A) Functions (F) Modeling (*) Geometry (G) Statistics and Probability (S)

Florida’s Numbering of the Common Core State Standards MACC.4.OA.2.4 Subject Grade Domain Cluster Standard MACC.912.N-RN.2.3 Subject Grade Category Domain Cluster Standard

MACC.4.OA Operations and Algebraic Thinking MACC.4.OA.2 Gain familiarity with factors and multiples MACC.4.OA.2.4Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Domain Cluster Standard

MACC.912.N Number and Quantity MACC.912.N-RN The Real Number System MACC.912.N-RN.2 Use properties of rational and irrational numbers MACC.912.N-RN.2.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Domain Cluster Standard Category

SAMPLE LESSON M/J MATHEMATICS 2 – RATIONAL NUMBERS The New “Look and Feel” of Instruction with Common Core Florida Dept. of EducationBureau of Curriculum & Instruction12 Please refer to sample lesson!

Course:Lesson Plan Sample Goal: Objective(s): Essential Question: Engaging Activity and Discussion Questions: Formative Assessment Task: Differentiated Instruction Strategies: 13

Learning Goal Students demonstrate proficiency with addition, subtraction, multiplication, and division of rational numbers expressed using decimals and fractions, and they are able to explain their thinking at a conceptual level. Florida Dept. of EducationBureau of Curriculum & Instruction14

Objective Students demonstrate fluency* when performing operations (addition, subtraction, multiplication, and division) with benchmark fractions and their decimal equivalents. Benchmark fractions include tenths, eighths, sixths, fifths, fourths, thirds, and halves. Florida Dept. of EducationBureau of Curriculum & Instruction15 *Fluency is the ability to compute flexibly, accurately, efficiently, and appropriately.

Essential Question Why is it important to build a sound foundation in your conceptual understanding of operations with fractions, and why is it just as important to recognize benchmark fractions and their decimal equivalents? Florida Dept. of EducationBureau of Curriculum & Instruction16

Performance Task Florida Dept. of EducationBureau of Curriculum & Instruction17

Course:M/J Math 2 ( ) Lesson Plan Sample Goal:Students demonstrate proficiency with addition, subtraction, multiplication, and division of rational numbers expressed using decimals and fractions, and they are able to explain their thinking at a conceptual level. Objective(s):Students demonstrate fluency when performing operations (addition, subtraction, multiplication, and division) with benchmark fractions and their decimal equivalents. Benchmark fractions include tenths, eighths, sixths, fifths, fourths, thirds, and halves. Essential Question: Why is it important to build a sound foundation in your conceptual understanding of operations with fractions, and why is it just as important to recognize benchmark fractions and their decimal equivalents? Engaging Activity and Discussion Questions: Students should be presented with the formative assessment task shown below and the teacher should read the question aloud. Initially, students should explore their thinking independently while making notes of interesting observations and/or any questions they may have. Students should then share their thinking with others in their small group; they should take turns asking questions of others, and adjust their own notes. Once everyone has had an opportunity to share their thinking and ask all their questions, students should once again work independently to finalize their response. Formative Assessment Task: Differentiated Instruction Strategies: Some students may need to explore the problem visually using grid paper or manipulatives such as Unifix cubes, fraction tiles, or a ruler. ELL students may need to use a bilingual dictionary to construct their response; they may also need to reference their glossary for this unit. Some students may need a hardcopy of the problem versus just projecting it on an overhead screen. 18

Discuss It! Based upon this lesson, how might you describe the new “look and feel” of instruction with Common Core? Florida Dept. of EducationBureau of Curriculum & Instruction19

Course Requirements and Standards Curriculum Mapping in Layers Florida Dept. of EducationBureau of Curriculum & Instruction20

Step 1 - Course Descriptions General Information – Course Code – Title – Credit – Graduation Requirement – Course Length Critical Areas of Focus or General Description NGSSS Requirements for Assessments Related Benchmarks – Common Core Literacy Standards – Common Core Mathematical Practices – Common Core Mathematics Standards Florida Dept. of EducationBureau of Curriculum & Instruction21

Critical Areas of Focus Florida Dept. of EducationBureau of Curriculum & Instruction22 Look at the Course Description for your selected grade level/course Read each critical area/unit As a group, summarize the main idea of each critical area in 1 – 2 sentences.

Grade 3 Math - Critical Areas of Focus 1.Developing understanding of multiplication and division and strategies for multiplication and division within Developing understanding of fractions, especially unit fractions (fractions with numerator 1) 3.Developing understanding of the structure of rectangular arrays and of area 4.Describing and analyzing two-dimensional shapes Florida Dept. of EducationBureau of Curriculum & Instruction23 Grade 3 Course Grade 3 Course

Course Requirements and Standards Curriculum Mapping in Layers “Chunks” or Big Ideas Florida Dept. of EducationBureau of Curriculum & Instruction24

Step 2 - “Chunking” Begin with the course descriptions and standards and benchmarks. “Chunk” the critical area into smaller major areas of focus. Sort the standards and/or benchmarks contained in the course description based upon these major areas of focus (there will likely be some overlapping of standards). Florida Dept. of EducationBureau of Curriculum & Instruction25

Grade 4– Critical Area #1 (1) Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.. Florida Dept. of EducationBureau of Curriculum & Instruction26

Grade 4“Chunking” Sample Critical Area 1: Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. In this unit: 1.Students apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. 2.Students develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. 3.Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.. Florida Dept. of EducationBureau of Curriculum & Instruction27

“Chunking” Standards 1.Students apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. – MACC.4.OA.1.1-MA.4.G.3.2 – MACC.4.OA.1.2-MACC.K12.MP.1.1 – MACC.4.OA.1.3-MACC.K12.MP.4.1 – MACC.4.OA.2.4-MACC.K12.MP.6.1 – MACC.4.NBT.2.5-MACC.K12.MP.7.1 – MACC.4.MD.1.1-MACC.K12.MP.8.1 – MACC.4.MD.1.3 Florida Dept. of EducationBureau of Curriculum & Instruction28

Course Requirements and Standards Curriculum Mapping in Layers “Chunks” or Big Ideas Florida Dept. of EducationBureau of Curriculum & Instruction29 Major Learning Goals

Step 3 - Learning Goals The Learning Goal (Defines what students should know and be able to do.) 1.Students demonstrate their understanding of multiplication by using various methods to compute products of multi-digit whole numbers. Students can accurately estimate or mentally calculate products. Florida Dept. of EducationBureau of Curriculum & Instruction30 The “Chunk” (Describes the integrated/related content standards students are expected to learn.) 1.Students apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products.

Learning Goals, Scales, and Learning Activities For more information: – – dex.aspx dex.aspx Florida Dept. of EducationBureau of Curriculum & Instruction31

State and Map Learning Goals Select one learning goal to share with group and using chart paper record the learning goal and “chunked” standards. Florida Dept. of EducationBureau of Curriculum & Instruction32

Learning Objectives Learning Objectives Learning Objectives Florida Dept. of EducationBureau of Curriculum & Instruction33 Mapping Learning Goals Learning Goal 1 Learning Goal 2 Learning Goal 3 Learning Goal 4

State and Map Learning Goals Begin the mapping process to identify when these learning goals will be taught using Curriculum Map. Florida Dept. of EducationBureau of Curriculum & Instruction34

Mathematics Curriculum Map Week/ Quarter LG6 LG7 LG5 LG1 LG2 2 LG1 LG2 LG5 LG6 LG7 3 LG5 LG6 4 LG5 LG6

Resources Florida Common Core – – Common Core State Standards for Mathematics – Solution Tree – tree.com/pdfs/Reproducibles_CCMLG/repros/table%202.2mathematicalpractices-- look-forsasclassroomindicators.pdfhttp://files.solution- tree.com/pdfs/Reproducibles_CCMLG/repros/table%202.2mathematicalpractices-- look-forsasclassroomindicators.pdf CPALMS – The Teaching Channel – Illustrative Mathematics – Inside Mathematics – Progressions Documents – 36

Resources Figure This – New York Times – to-apply-algebra-with-the-new-york-times/ to-apply-algebra-with-the-new-york-times/ NCTM Illuminations NCTM Navigation Series – 37

Objectives for Day 1 – Status Check Participants will: Identify major learning goals for a specific course by integrating across content areas and “chunking” the standards into a few big ideas, and Develop a projected timeline for instruction by mapping the major learning goals across the semester or year as appropriate for the course. Florida Dept. of EducationBureau of Curriculum & Instruction38

Reflections What are you most excited by with the transition to CCSS? What concerns you the most about the transition to CCSS? How will you try to address these concerns? Florida Dept. of EducationBureau of Curriculum & Instruction39